Anyway, this anecdote doesn't fit with the field and it's at best a really rare exception, not representative and not relevant. So I found it dishonest to bring it up like that in this context.
So how do you as a small business owner even know whether the agency you pay 10k is giving you good and maintainable code?
in 2 years when you want changes you'll realise that no one wants to work on this or if they do, they will ask much more, and the previous agency might be willing to take it on, but they will have the leverage to ask even more.
Like in any other industry: you network and connect and consult with people before knocking on any random agency door.
I don't ring a random plumber, I ask a friend or two if they know someone who's reliable.
Also, you need to add maintenance to your budget.
It's like insisting that you won't get a car to take you to the supermarket for less than $200k based on experience of enquiring about the availability of cheap runarounds but only at supercar dealerships
And if you actually need something hand rolled using authentic vanilla HTML and artisanal node frameworks you can still get it for less than $200k :)